A geologic model is a digital representation of the detailed internal geometry and rock properties of a subsurface earth volume, such as a petroleum reservoir or a sediment-filled basin. In the oil and gas industry, geologic models provide geologic input to reservoir performance simulations which are used to select locations for new wells, estimate hydrocarbon reserves, and plan reservoir-development strategies. The spatial distribution of permeability is a key parameter in characterizing reservoir performance, and, together with other rock and fluid properties, determines the producibility of the reservoir. For sandstone reservoirs, the spatial distribution of permeability is a function of the grain-size distribution of sands which compose the reservoir, the compartmentalization of those sands by barriers of finer grained material, and the mineralogy and burial history of the reservoir.
Most geologic models built for petroleum applications are in the form of a three-dimensional array of model blocks (cells), to which geologic and/or geophysical properties such as lithology, porosity, acoustic impedance, permeability, and water saturation are assigned (such properties will be referred to collectively herein as “rock properties”). The entire set of model blocks represents the subsurface earth volume of interest. The goal of the geologic-modeling process is to assign rock properties to each model block in the geologic model.
The geologic modeling process can use many different data types, including but not limited to rock-property data obtained from cores, well logs, seismic data, well test and production data, and structural and stratigraphic surfaces that define distinct zones within the model. In general, the resolution or spatial coverage of the available data is not adequate to uniquely determine the rock properties in every geologic model cell. Other assumptions about the variability in these properties are made in order to populate all model cells with reasonable property values. Geocellular techniques, object-based modeling, and process modeling are three main ways to populate the discretized geologic volume with properties.
Geocellular models: In the geocellular approach, the relationship between properties in nearby cells is specified statistically. Geostatistical estimation methods (which may be either deterministic or probabilistic) are used to compute rock property values within cells. These methods take into account distance, direction, and spatial continuity of the rock property being modeled. Deterministic estimation methods commonly calculate a minimum-variance estimate of the rock property at each block. Probabilistic estimation methods develop distributions of the rock-property values and produce a suite of geologic model realizations for the rock property being modeled, with each realization theoretically being equally probable. The spatial continuity of a rock property may be captured by a variogram, a well-known technique for quantifying the variability of a rock property as a function of separation distance and direction. U.S. Pat. Nos. 5,838,634, 6,381,543 and 6,480,790 cover geocellular modeling methods embodied in processing flows which include repetitive optimization steps to drive the geologic model toward conformance with geologic and geophysical data types such as wells, seismic surveys and subsurface fluid production and pressure data. Most commercial modeling software packages, including PETREL, GOCAD and STRATAMODEL, contain a wide spectrum of geostatistical tools designed to fulfill the requirements of reservoir geologists and engineers. While these methods can readily accommodate data control points such as wells and geophysical constraints such as seismic data, they generally do not closely replicate the geologic structures observed in natural systems.
Object-based models: In the object-based approach, subsurface reservoir volumes are treated as assemblages of geologic objects with pre-defined forms such as channels and depositional lobes. U.S. Pat. No. 6,044,328 discloses one object-based modeling scheme that allows geologists and reservoir engineers to select geologic objects from an analog library to best match the reservoir being modeled. The appropriateness of the analog is judged by the operator of the process based on their geologic experience. Most commercial software packages including PETREL, IRAP-RMS and GOCAD implement objects as volumetric elements that mimic channels and lobes using simplified elements based on user deformable shapes such as half pipes and ellipses. Other examples of object-based models are the model of Mackey and Bridge (1995) and the model of Webb (1994). In their models, the depositional objects, such as a river belt in the model of Mackey and Bridge (1995) and the braided stream network in the model of Webb (1994), are placed sequentially on top of each other according to some algorithms. While these models try to mimic the real depositional structures, they do not attempt to capture the physics of water flow and sediment transport that, over geologic time, determined the rock properties at a particular subsurface location.
Process Models: Process-based models attempt to reproduce subsurface stratigraphy by building sedimentary deposits in chronological order relying to varying degrees on a model or approximation of the physical processes shaping the geology. While process-based models could potentially provide the most accurate representation of geologic structures, their application is complicated by the difficulty in matching their results to data control points or seismic images. Application of process models to predicting rock properties generally involves checking the model against subsurface data and then rerunning the model with new control variables in an iterative process. Although process models are rarely used in current industrial practice, U.S. Pat. Nos. 5,844,799, 6,205,402 and 6,246,963 describe three such methods. These methods employ diffusion or rule-based process models to create basin-scale models with limited spatial detail inadequate for reservoir performance simulation.
A number of academic publications exist on process-based modeling of stratigraphy, particularly in shallow water environments. Most of these methods are not derived from the physics of the depositing fluid flow and sediment transport. Rather, transport of sediments is approximated by a diffusion-like equation. Examples of models in this class include the model of Bowman and Vail (1999), which is a two-dimensional algorithmic model based on a set of empirical rules for a shallow water environment, the model of Granjeon and Joseph (1999) which is a three-dimensional model for simulation of stratigraphy in shallow water environments, the model of Kaufman et al. (1991) which has been used in their simulation of sedimentation in shallow marine depositional systems, and the model of Ritchie et al. (1999, 2004ab) which was used in their work on three-dimensional numerical modeling of deltaic depositional sequences.
Different from the models described above, the SEDSIM model of Tetzlaff and Harbaugh (1989) simulates clastic sedimentation in the shallow water environment by solving two-dimensional depth-averaged flow equations using the Marker-in-cell [Harlow, 1964], or particle-in-cell method [Hockney and Eastwood, 1981]. Although SEDSIM was originally designed for the shallow water environment, it has also been applied to simulate a turbidity current by modifying the gravitational constant to take into account the relative density of the flow with respect to the surrounding medium [Tetzlaff and Harbaugh, 1989]. However, SEDSIM does not include the entrainment of water by turbidity currents and the resulting flow expansion and impact on sediment deposition. Since SEDSIM uses the Markering-Cell Method and the flow is represented by many flow elements with constant volume, to add the water entrainment relationship would involve significant modifications of SEDSIM.
The gridding scheme of SEDSIM imposes some limitations. The vertical dimension of each three-dimensional cell that contains sediment is fixed. In addition, each cell can only contain a specific single type (or size) of sediment and only the top-most cell can participate in the process of erosion.
Sediment transport and its effect on the flow are sometimes inaccurately modeled in SEDSIM. The reasons include not using experimentally-based erosion functions, and not allowing, the finer material within the flow to deposit until all the coarser material in excess of the transport capacity of the flow has been deposited. In addition, SEDSIM does not correct for depositional porosity in modeling of deposit elevation so the deposit elevation is underestimated. The effect of spatially and temporally varying sediment concentration on the gravitational driving forces is also not modeled.
Syvitski et al. (1999) published a process-based model for simulating the movement of sediments onto continental margins and their preservation in the stratigraphic record. There are many components in the model of Syvitski et al. (1999). They include (1) river mouth process, (2) buoyant river plumes and hyperpycnal flows, (3) turbidity currents, (4) currents and waves, and (5) debris flows generated from slope instabilities.
The mathematical model to describe the hyperpycnal flows and turbidity currents used by Syvitski et al. (1999) in their model is essentially an improved version of the standard Chezy's uniform flow model for a turbidity current [Mulder, T., J. Syvitski, and K. I. Skene, 1998; Bagnold 1954, 1966; Komar, 1971, 1973, 1977; Bowen et al. 1984; Piper and Savoye 1993]. In Chezy's uniform flow model, the sum of the gravitational driving force, the frictional resistance to flow, and the internal friction of the flow is assumed to be zero. By contrast, in Syvitski et al. (1999), the sum of the three forces is (more accurately) assumed to equal the acceleration of the current.
The hyperpycnal flow and turbidity current model used by Syvitski et al. (1999) is a large (basin) scale approximation of the flow. As such, it contains many assumptions that prevent accurate prediction of the finer-scale sedimentary structures that may control the performance of hydrocarbon reservoirs. For example, in their model, the convection of the flow momentum is not represented. The vast majority of sedimentary bodies that form oil and gas reservoirs are jet and leaf deposits [VanWagoner et al. 2003], at which scale the convection of flow momentum plays a crucial role in determining the dynamics of the flow and the nature of the bodies. Also, the slope of the interface between the turbid and clear water is approximated by the bed slope in their calculation of the gravitational driving forces. This prevents the model from capturing the backwater effect and hydraulic jumps in the flow, which are mechanisms in triggering avulsion and filling mini-basins [Beaubouef and Friedman, 2000]. Without these mechanisms, application of their model in simulating oil and gas reservoirs is limited since avulsion is one of the key processes responsible for reservoir heterogeneities.
The hyperpycnal flow and turbidity current model of Svyitski et al. (1999) is fundamentally one-dimensional and therefore cannot accurately represent lateral variability in rock properties or the physics of the three-dimensional flow that creates many characteristic features of deep water sediment stratigraphy as shown by Van Wagoner et al. (2003). Their model describes the confined flow of a turbidity current down a one-dimensional conduit. The widths of the conduit have to be specified before hand since there is no capability for modeling the initiation and evolution of channels and their associated channel deposits, which is another key element in oil and gas reservoirs. Finally, the Syvitski et al. (1999) model decouples the interaction between flow and deposit.
In their studies of self-accelerating turbidity currents, Parker et al. (1986) derived two sets of mathematic equations to describe the flow of turbidity currents in the deep-water environment. The first set of equations is called the “three-equation” model. The second set of equations is called the “four-equation” model. Both sets of equations are depth-averaged equations, and both consist of equations for the conservation of flow momentum, flow mass, and sediment. The “four-equation” model differs from the “three-equation” model in that it also explicitly takes the generation, dissipation, and transport of the turbulent kinetic energy into account. Neither model has been combined with the capability to record sedimentary information about the resulting deposit.
The mathematical formulation of Parker et al. (1986) was originally derived for one-dimensional flow with a single sediment grain-size. The “three-equation” model has later been extended to 2 dimension and multiple grain sizes by Bradford (1996, Ph.D. thesis), Bradford et al. (1997), Imran and Parker (1998) and Bradford and Katopodes (1999a,b).
Both Imran and Parker (1998) and Bradford and Katopodes (1999a,b) have applied the extended “three-equation” model of Parker et al. (1986) to study turbidity currents and incipient channelization in the deep water environment. In both studies, only the bathymetries of deposits in the earliest stages of development [Van Wagoner et al. 2003] have been reported. Imran and Parker (1998) discussed the inability of their model to simulate the longer-term evolution of the bathymetry of the deposits, saying “at some point, levee height would approach the thickness of the turbidity current itself. The present scheme would fail whenever levees grew to the point of nearly completely channelizing the flow, allowing for only small spillover of the turbidity current.” Neither the work of Imran and Parker (1998) nor that of Bradford (1997) and Bradford and Katopodes (1999a,b) is related to the simulation of the three-dimensional stratigraphy of sedimentary deposits and their associated sedimentary bodies and rock properties as shall be described in this invention.
Accordingly, there is a need to modify both the “three-equation” model and the “four-equation” model for the turbidity currents of Parker et al. (1986) to simulate the long-term evolution of the sedimentary systems, and to simulate the formation of the three-dimensional stratigraphy for deep water deposits. In addition, there is a need for a method that honors the shapes and property distributions of naturally occurring sedimentary deposits based on geologic data such as seismic and well data. Such a method may be based on the fundamental laws of physics for water and sediment transport and incorporate features from process, object-based and geostatistical approaches. Preferably, such a procedure should provide an automated option so that the optimization process can be performed by a computer, resulting in a more accurate model of the subsurface volume of interest, with negligible additional time and effort. The present invention satisfies this need.